Transverse velocities and shear stresses in river bends
Type of content
Expressions are presented for the transverse velocity profile and the transverse bed shear stress in a channel bend. These expressions are obtained from the momentum equations by assuming a logarithmic longitudinal velocity profile. The boundary conditions and expressions for eddy viscosity are consistent with the logarithmic longitudinal velocity profile. As a result, the transverse bed shear stress can be calculated without the need to use ratios of near-bed or slip velocities. The influence of non-zero depth-averaged velocities are included in the expressions. As a result, the expressions for the transverse velocity profile and transverse bed shear stress are not limited to situations of fully developed bend flow, as is the case with several previous profiles. The expression for the transverse velocity profile is verified by field experiments using acoustic doppler velocimeters to measure velocity profiles in two stream bends. A simple meandering stream bed topography model is developed illustrating how the expressions for transverse shear stress can be used. This topography model uses an analytical solution to the depth-averaged momentum and continuity equations to calculate depth_-averaged velocities. The shear stresses are calculated using the method presented in the thesis. Topography is calculated from sediment continuity. The use of a sine-generated curve to describe river meander geometry is briefly discussed. Regime equations are combined to give predictions of meander geometry from a known discharge and valley slope. Finally, results of experiments exploring behaviour of meandering channels in a sand tray are presented, illustrating various aspects of bed hydraulics and sediment movement.